Effect of heat source/sink on MHD free convection flow in a channel filled with nanofluid in the existence of induced magnetic field: an analytic approach

An attempt to examine the relevance of heat source/sink on magnetohydrodynamics free convection flow in a vertical channel with an induced magnetic field is achieved. The analytical solution to the set of the differential equation is obtained by perturbation method for small thermophoresis and Brownian diffusion parameters under the unified thermal boundary condition (isothermal and isoflux boundary condition) for the energy equation. Numerical solution to the flow equation is also obtained by incorporating RKF45 in Maple software. The influence of active parameters such as Hartman number (Ha), magnetic Prandtl number (Pm), heat source/sink parameter (± S), Buoyancy ratio (Br), Brownian motion (Nb) and thermophoretic parameter (Nt) on velocity, induced magnetic field, induced current density, nanoparticles concentration, temperature and skin friction are depicted and discussed in detail. Results reveal that the Brownian motion parameter (Nb) and Buoyancy ratio (Br) augment enhances the shear stress whereas the contrast is observed with Hartman number (Ha) and thermophoretic parameter (Nt). Results also reveal that Hartman number (Ha) and thermophoretic parameter (Nt) enhances the induced current density while the contrast is true for heat sink parameter (−S). Finally, the temperature of the nanofluid could be enhanced with increase in Brownian motion parameter (Nb) and heat source parameter (+ S).